Hadley Cycles what powers the trade winds? The Earth\'s trade winds arise from t

Question

Hadley Cycles what powers the trade winds? The Earth's trade winds arise from the differences in buoyancy between hot air and cold air. Air is heated at the Earth's surface near the equator (see (1) in Figure 7.10), lowering its density; the air rises (2), pushing upper air away toward the Northern latitudes, where the air cools (3); then the air drops back down to Earth (4).pushing the cold surface air back toward the equator. Consider an imaginary balloon containing 1 m^3 of an ideal gas. At p = 1 atm and T = 300 K, what is the number of moles n of air contained in the balloon? If that balloon of n moles of air remains at p = l atm but is now heated to T = 330K, its volume increases. What is the new density p - n/V? Assuming no heat transfer, how high will the balloon in part (b) rise? Use Figure 10.2 to make a rough guess (Useful conversion: 1 atm 1 bar).

Explanation / Answer

As per Ideal gas equation, P*V = n*R*T ; we get, where P = pressure in atm , V = volume in litres (1m3 = 1000 litres),

R = universal gas constant, T = temperature in kelvin

a) 1*1000 = n*0.0821*300

or, n = moles of the gas = 40.601

b) Since, pressure and mole of the gas remains constant, therefore

V1/T1 = V2/T2

or, 1000/300 = V2/330

OR, new volume, V2 = 1100 litres = 1.1 m3

c) increase in volume = 0.1 m3 = 100 litres

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